{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourier Neural Operator 1D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\s1612415\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\tqdm\\auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "## Imports \n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import torch \n",
    "import torch.nn as nn\n",
    "from timeit import default_timer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Set seeds\n",
    "torch.manual_seed(0)\n",
    "np.random.seed(0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Data"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Heat Equation:\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial u}{\\partial t} &= \\alpha \\frac{\\partial^2 u}{\\partial x^2} \\\\\n",
    "u(x, 0) &= x^2 \\\\\n",
    "u(0, t) &= u(1, t) = 2 - \\exp(-t)\n",
    "\\end{align*}\n",
    "\n",
    "Solution: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: Create Heat Equation Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Steps in x direction\n",
    "nx = 200\n",
    "## Steps in t direction\n",
    "nt = 100\n",
    "\n",
    "h = 1 / nx ## Step size in x direction\n",
    "k = 1 / nt ## Step size in t direction\n",
    "\n",
    "alpha = 0.05\n",
    "r =  alpha * k / h**2\n",
    "\n",
    "X, T = np.meshgrid(np.linspace(0, 1, nx + 1), np.linspace(0, 1, nt + 1))\n",
    "\n",
    "plt.scatter(X, T)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Initial Condition\n",
    "beta = np.pi\n",
    "u0 = np.sin(beta * X[0]) \n",
    "\n",
    "## Boundary Conditions\n",
    "ux0 = 0 # u0[0] # T[:, 0]\n",
    "uxn = 0 # u0[-1] # 2 - np.exp(-T[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.zeros((nx - 1, nx - 1))\n",
    "B = np.zeros((nx - 1, nx - 1))\n",
    "\n",
    "for i in range(nx - 1):\n",
    "    A[i, i] = 2 + 2 * r\n",
    "    B[i, i] = 2 - 2 * r\n",
    "\n",
    "for i in range(nx - 2):\n",
    "    A[i + 1, i] = -r\n",
    "    A[i, i + 1] = -r\n",
    "    B[i + 1, i] = r\n",
    "    B[i, i + 1] = r\n",
    "\n",
    "Ainv = np.linalg.inv(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Compute Solution\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "# b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    # b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    # b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx])) # + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(u, aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Number of Samples \n",
    "n = 10000\n",
    "## Output\n",
    "data_in = []\n",
    "data_out = []\n",
    "\n",
    "## Generate Data\n",
    "for _ in range(n):\n",
    "    beta = np.random.uniform(-10, 10)\n",
    "    beta_vec = beta * np.ones(201)\n",
    "\n",
    "    u0 = np.sin(beta * X[0])\n",
    "\n",
    "    data_in.append([beta_vec , np.arange(0, 1.005, 0.005)])\n",
    "\n",
    "    ## Create Solution Matrix\n",
    "    u = np.zeros((nt + 1, nx + 1))\n",
    "    u[0] = u0\n",
    "    u[:, 0] = ux0\n",
    "    u[:, -1] = uxn\n",
    "\n",
    "    # b = np.zeros(nx - 1)\n",
    "    for j in range(1, nt + 1):\n",
    "        # b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "        # b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "        u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx])) # + b)\n",
    "\n",
    "    data_out.append(u[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\s1612415\\AppData\\Local\\Temp\\ipykernel_20996\\974941267.py:1: UserWarning: Creating a tensor from a list of numpy.ndarrays is extremely slow. Please consider converting the list to a single numpy.ndarray with numpy.array() before converting to a tensor. (Triggered internally at ..\\torch\\csrc\\utils\\tensor_new.cpp:233.)\n",
      "  data_in = np.array(torch.tensor(data_in).float())\n"
     ]
    }
   ],
   "source": [
    "data_in = np.array(torch.tensor(data_in).float())\n",
    "data_out = np.array(torch.tensor(data_out).float().unsqueeze(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Data Loader\n",
    "from torch.utils.data import Dataset, DataLoader\n",
    "import pandas as pd\n",
    "\n",
    "class CustomDataset(Dataset):\n",
    "    def __init__(self, t, x):\n",
    "        self.t = t\n",
    "        self.x = x\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.t)\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        return self.t[index], self.x[index]\n",
    "\n",
    "data = CustomDataset(data_in, data_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701, 0.9762701,\n",
       "        0.9762701, 0.9762701, 0.9762701],\n",
       "       [0.       , 0.005    , 0.01     , 0.015    , 0.02     , 0.025    ,\n",
       "        0.03     , 0.035    , 0.04     , 0.045    , 0.05     , 0.055    ,\n",
       "        0.06     , 0.065    , 0.07     , 0.075    , 0.08     , 0.085    ,\n",
       "        0.09     , 0.095    , 0.1      , 0.105    , 0.11     , 0.115    ,\n",
       "        0.12     , 0.125    , 0.13     , 0.135    , 0.14     , 0.145    ,\n",
       "        0.15     , 0.155    , 0.16     , 0.165    , 0.17     , 0.175    ,\n",
       "        0.18     , 0.185    , 0.19     , 0.195    , 0.2      , 0.205    ,\n",
       "        0.21     , 0.215    , 0.22     , 0.225    , 0.23     , 0.235    ,\n",
       "        0.24     , 0.245    , 0.25     , 0.255    , 0.26     , 0.265    ,\n",
       "        0.27     , 0.275    , 0.28     , 0.285    , 0.29     , 0.295    ,\n",
       "        0.3      , 0.305    , 0.31     , 0.315    , 0.32     , 0.325    ,\n",
       "        0.33     , 0.335    , 0.34     , 0.345    , 0.35     , 0.355    ,\n",
       "        0.36     , 0.365    , 0.37     , 0.375    , 0.38     , 0.385    ,\n",
       "        0.39     , 0.395    , 0.4      , 0.405    , 0.41     , 0.415    ,\n",
       "        0.42     , 0.425    , 0.43     , 0.435    , 0.44     , 0.445    ,\n",
       "        0.45     , 0.455    , 0.46     , 0.465    , 0.47     , 0.475    ,\n",
       "        0.48     , 0.485    , 0.49     , 0.495    , 0.5      , 0.505    ,\n",
       "        0.51     , 0.515    , 0.52     , 0.525    , 0.53     , 0.535    ,\n",
       "        0.54     , 0.545    , 0.55     , 0.555    , 0.56     , 0.565    ,\n",
       "        0.57     , 0.575    , 0.58     , 0.585    , 0.59     , 0.595    ,\n",
       "        0.6      , 0.605    , 0.61     , 0.615    , 0.62     , 0.625    ,\n",
       "        0.63     , 0.635    , 0.64     , 0.645    , 0.65     , 0.655    ,\n",
       "        0.66     , 0.665    , 0.67     , 0.675    , 0.68     , 0.685    ,\n",
       "        0.69     , 0.695    , 0.7      , 0.705    , 0.71     , 0.715    ,\n",
       "        0.72     , 0.725    , 0.73     , 0.735    , 0.74     , 0.745    ,\n",
       "        0.75     , 0.755    , 0.76     , 0.765    , 0.77     , 0.775    ,\n",
       "        0.78     , 0.785    , 0.79     , 0.795    , 0.8      , 0.805    ,\n",
       "        0.81     , 0.815    , 0.82     , 0.825    , 0.83     , 0.835    ,\n",
       "        0.84     , 0.845    , 0.85     , 0.855    , 0.86     , 0.865    ,\n",
       "        0.87     , 0.875    , 0.88     , 0.885    , 0.89     , 0.895    ,\n",
       "        0.9      , 0.905    , 0.91     , 0.915    , 0.92     , 0.925    ,\n",
       "        0.93     , 0.935    , 0.94     , 0.945    , 0.95     , 0.955    ,\n",
       "        0.96     , 0.965    , 0.97     , 0.975    , 0.98     , 0.985    ,\n",
       "        0.99     , 0.995    , 1.       ]], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 201)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[0][0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataloader = DataLoader(data, batch_size=16, shuffle=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cpu device.\n"
     ]
    }
   ],
   "source": [
    "## Get Device for Training\n",
    "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "print(f'Using {device} device.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Fourier Integral Kernel 1D\n",
    "class FourierIntegralKernel1D(nn.Module):\n",
    "    def __init__(self, in_channels: int, out_channels: int, modes: int):\n",
    "        super(FourierIntegralKernel1D, self).__init__()\n",
    "        '''\n",
    "        '''\n",
    "        self.in_channels = in_channels\n",
    "        self.out_channels = out_channels \n",
    "        self.modes = modes \n",
    "        ## Set (random) weights for the linear transform\n",
    "        weights = torch.rand(self.modes, self.out_channels, self.in_channels, dtype=torch.cfloat) \n",
    "        self.weights = nn.Parameter(weights / (self.in_channels * self.out_channels)) ## Optional: Scale weights\n",
    "\n",
    "    def forward(self, v: torch.Tensor) -> torch.Tensor:\n",
    "        '''\n",
    "        FFT -> Linear Transform -> Inverse FFT\n",
    "        '''\n",
    "        ## FFT\n",
    "        v_rfft = torch.fft.rfft(v) \n",
    "\n",
    "        ## Linear Transform \n",
    "        lv_rfft = torch.zeros(v_rfft.shape, dtype=torch.cfloat)\n",
    "        lv_rfft[:, :, :self.modes] = torch.einsum('koi, bki -> bko', self.weights, v_rfft[:, :, :self.modes].permute(0, 2, 1)).permute(0, 2, 1) ## TODO: Should I have 5 dimensions here?\n",
    "        \n",
    "        ## Inverse FFT\n",
    "        v2 = torch.fft.irfft(lv_rfft, n=v.shape[-1])\n",
    "        return v2\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Fourier Network Operator 1D\n",
    "class FourierNetworkOperator1D(nn.Module):\n",
    "    def __init__(self, da: int, du: int, width: int, modes: int):\n",
    "        super(FourierNetworkOperator1D, self).__init__()\n",
    "        '''\n",
    "        '''\n",
    "        self.width = width\n",
    "        self.modes = modes\n",
    "\n",
    "        ## P: Lifts the lower dimensional function to higher dimensional space\n",
    "        self.P = nn.Conv1d(da, self.width, 1) ## TODO: Change da\n",
    "\n",
    "        ## K: Fourier integral kernel operator\n",
    "        self.k0 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        self.k1 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        self.k2 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        self.k3 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k4 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k5 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k6 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k7 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k8 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "        # self.k9 = FourierIntegralKernel1D(self.width, self.width, self.modes)\n",
    "\n",
    "        ## W: Pointwise linear operator\n",
    "        self.w0 = nn.Conv1d(self.width, self.width, 1)\n",
    "        self.w1 = nn.Conv1d(self.width, self.width, 1)\n",
    "        self.w2 = nn.Conv1d(self.width, self.width, 1)\n",
    "        self.w3 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w4 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w5 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w6 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w7 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w8 = nn.Conv1d(self.width, self.width, 1)\n",
    "        # self.w9 = nn.Conv1d(self.width, self.width, 1)\n",
    "\n",
    "        ## Q: Projects the higher dimensional function to lower dimensional space\n",
    "        self.Q = nn.Conv1d(self.width, du, 1) ## TODO: Change du\n",
    "\n",
    "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
    "        '''\n",
    "        '''\n",
    "        ## P\n",
    "        x = self.P(x)\n",
    "\n",
    "        ## Fourier Layer #0\n",
    "        ## K\n",
    "        x1 = self.k0(x)\n",
    "        ## W\n",
    "        x2 = self.w0(x)\n",
    "        ## Sum\n",
    "        x = x1 + x2\n",
    "        ## Gelu\n",
    "        x = nn.functional.gelu(x)\n",
    "        # x = nn.functional.gelu(x1)\n",
    "        # x = nn.functional.gelu(x2)\n",
    "\n",
    "        ## Fourier Layer #1\n",
    "        ## K\n",
    "        x1 = self.k1(x)\n",
    "        ## W\n",
    "        x2 = self.w1(x)\n",
    "        ## Sum \n",
    "        x = x1 + x2\n",
    "        ## Gelu\n",
    "        x = nn.functional.gelu(x)\n",
    "        # x = nn.functional.gelu(x1)\n",
    "        # x = nn.functional.gelu(x2)\n",
    "\n",
    "        ## Fourier Layer #2\n",
    "        ## K\n",
    "        x1 = self.k2(x)\n",
    "        ## W\n",
    "        x2 = self.w2(x)\n",
    "        ## Sum\n",
    "        x = x1 + x2\n",
    "        ## Gelu\n",
    "        x = nn.functional.gelu(x)\n",
    "        # x = nn.functional.gelu(x1)\n",
    "        # x = nn.functional.gelu(x2)\n",
    "\n",
    "        ## Fourier Layer #3\n",
    "        ## K\n",
    "        x1 = self.k3(x)\n",
    "        ## W\n",
    "        x2 = self.w3(x)\n",
    "        ## Sum\n",
    "        x = x1 + x2\n",
    "        ## Gelu\n",
    "        x = nn.functional.gelu(x)\n",
    "        # x = nn.functional.gelu(x1)\n",
    "        # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #4\n",
    "        # ## K\n",
    "        # x1 = self.k4(x)\n",
    "        # ## W\n",
    "        # x2 = self.w4(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #5\n",
    "        # ## K\n",
    "        # x1 = self.k5(x)\n",
    "        # ## W\n",
    "        # x2 = self.w5(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #6\n",
    "        # ## K\n",
    "        # x1 = self.k6(x)\n",
    "        # ## W\n",
    "        # x2 = self.w6(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #7\n",
    "        # ## K\n",
    "        # x1 = self.k7(x)\n",
    "        # ## W\n",
    "        # x2 = self.w7(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #8\n",
    "        # ## K\n",
    "        # x1 = self.k8(x)\n",
    "        # ## W\n",
    "        # x2 = self.w8(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        # ## Fourier Layer #9\n",
    "        # ## K\n",
    "        # x1 = self.k9(x)\n",
    "        # ## W\n",
    "        # x2 = self.w9(x)\n",
    "        # ## Sum\n",
    "        # x = x1 + x2\n",
    "        # ## Gelu\n",
    "        # x = nn.functional.gelu(x)\n",
    "        # # x = nn.functional.gelu(x1)\n",
    "        # # x = nn.functional.gelu(x2)\n",
    "\n",
    "        ## Q\n",
    "        x = self.Q(x)\n",
    "        return x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import operator\n",
    "# from functools import reduce\n",
    "\n",
    "# def count_parameters(model):\n",
    "#     c = 0\n",
    "#     for p in list(model.parameters()):\n",
    "#         c += reduce(operator.mul, list(p.size() + (2, ) if p.is_complex() else p.size()))\n",
    "#     return c\n",
    "\n",
    "# model = FourierNetworkOperator1D(2, 1, width=64, modes=4)\n",
    "# print(f'Number of parameters: {count_parameters(model)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P.weight: 128\n",
      "P.bias: 64\n",
      "k0.weights: 65536\n",
      "k1.weights: 65536\n",
      "k2.weights: 65536\n",
      "k3.weights: 65536\n",
      "w0.weight: 4096\n",
      "w0.bias: 64\n",
      "w1.weight: 4096\n",
      "w1.bias: 64\n",
      "w2.weight: 4096\n",
      "w2.bias: 64\n",
      "w3.weight: 4096\n",
      "w3.bias: 64\n",
      "Q.weight: 64\n",
      "Q.bias: 1\n",
      "Total Trainable Params: 279041\n"
     ]
    }
   ],
   "source": [
    "def count_parameters(model):\n",
    "    total_params = 0\n",
    "    for name, parameter in model.named_parameters():\n",
    "        if not parameter.requires_grad: continue\n",
    "        params = parameter.numel()\n",
    "        print(f'{name}: {params}')\n",
    "        total_params+=params\n",
    "    print(f\"Total Trainable Params: {total_params}\")\n",
    "    return total_params\n",
    "    \n",
    "model = FourierNetworkOperator1D(2, 1, width=64, modes=16)\n",
    "num_parameters = count_parameters(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.0001+0.0001j, grad_fn=<MeanBackward0>)\n",
      "tensor(9.9577e-05, grad_fn=<StdBackward0>)\n"
     ]
    }
   ],
   "source": [
    "print(torch.mean(model.k0.weights))\n",
    "print(torch.std(model.k0.weights))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Model Parameters\n",
    "learning_rate = 1e-3\n",
    "epochs = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Loss Function\n",
    "loss_function = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Optimizer \n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "vec = torch.from_numpy(np.arange(0, 1.005, 0.005)).float().unsqueeze(0).unsqueeze(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta: 6.143844901770926\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 0\n",
    "beta0 = np.random.uniform(-10, 10)\n",
    "print(f'beta: {beta0}')\n",
    "beta0_vec = torch.from_numpy(beta0 * np.ones(201)).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u0 = torch.from_numpy(np.sin(beta0 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta0_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta0_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta: 4.115054390602959\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 1\n",
    "beta1 = np.random.uniform(-10, 10)\n",
    "print(f'beta: {beta1}')\n",
    "beta1_vec = torch.from_numpy(beta1 * np.ones(201)).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u0 = torch.from_numpy(np.sin(beta1 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta1_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta1_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta: -9.968876041407357\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 2\n",
    "beta2 = np.random.uniform(-10, 10)\n",
    "print(f'beta: {beta2}')\n",
    "beta2_vec = torch.from_numpy(beta2 * np.ones(201)).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u0 = torch.from_numpy(np.sin(beta2 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta2_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta2_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Training Loop\n",
    "def train_loop(dataloader, model, loss_function, optimizer):\n",
    "    size = len(dataloader.dataset)\n",
    "    for batch, (t, x) in enumerate(dataloader):\n",
    "        # Compute prediction and loss\n",
    "        pred = model(t)\n",
    "        loss = loss_function(pred, x)\n",
    "\n",
    "        # Backpropagation\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "        if batch % 100 == 0:\n",
    "            loss, current = loss.item(), batch * len(t)\n",
    "            print(f\"loss: {loss:>7f}  [{current:>5d}/{size:>5d}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1\n",
      "-------------------------------\n",
      "loss: 0.053883  [    0/10000]\n",
      "loss: 0.000546  [ 1600/10000]\n",
      "loss: 0.000042  [ 3200/10000]\n",
      "loss: 0.000037  [ 4800/10000]\n",
      "loss: 0.000031  [ 6400/10000]\n",
      "loss: 0.001042  [ 8000/10000]\n",
      "loss: 0.000023  [ 9600/10000]\n",
      "Epoch 2\n",
      "-------------------------------\n",
      "loss: 0.000030  [    0/10000]\n",
      "loss: 0.000025  [ 1600/10000]\n",
      "loss: 0.000096  [ 3200/10000]\n",
      "loss: 0.000022  [ 4800/10000]\n",
      "loss: 0.000011  [ 6400/10000]\n",
      "loss: 0.000301  [ 8000/10000]\n",
      "loss: 0.000016  [ 9600/10000]\n",
      "Epoch 3\n",
      "-------------------------------\n",
      "loss: 0.000008  [    0/10000]\n",
      "loss: 0.000086  [ 1600/10000]\n",
      "loss: 0.000077  [ 3200/10000]\n",
      "loss: 0.000028  [ 4800/10000]\n",
      "loss: 0.000016  [ 6400/10000]\n",
      "loss: 0.000065  [ 8000/10000]\n",
      "loss: 0.000046  [ 9600/10000]\n",
      "Epoch 4\n",
      "-------------------------------\n",
      "loss: 0.000006  [    0/10000]\n",
      "loss: 0.000008  [ 1600/10000]\n",
      "loss: 0.000035  [ 3200/10000]\n",
      "loss: 0.000112  [ 4800/10000]\n",
      "loss: 0.000031  [ 6400/10000]\n",
      "loss: 0.000055  [ 8000/10000]\n",
      "loss: 0.000051  [ 9600/10000]\n",
      "Epoch 5\n",
      "-------------------------------\n",
      "loss: 0.000018  [    0/10000]\n",
      "loss: 0.000019  [ 1600/10000]\n",
      "loss: 0.000003  [ 3200/10000]\n",
      "loss: 0.000006  [ 4800/10000]\n",
      "loss: 0.000017  [ 6400/10000]\n",
      "loss: 0.000009  [ 8000/10000]\n",
      "loss: 0.000011  [ 9600/10000]\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "for t in range(epochs):\n",
    "    print(f\"Epoch {t+1}\\n-------------------------------\")\n",
    "    train_loop(dataloader, model, loss_function, optimizer)\n",
    "print(\"Done!\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 0\n",
    "u0 = torch.from_numpy(np.sin(beta0 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta0_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta0_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 1\n",
    "u0 = torch.from_numpy(np.sin(beta1 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta1_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta1_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vXBe787l2l0gAEhzlOHl0O5A63nt7IyIi3TBZ7NhbKuHXAmv1eMpIoSq8JCUlISkpyeO6rKwsVFZWYvfu3RgyZAgAYPPmzXA6ncjMzOzYTgOcaOM62541MF06ioW7RETUislix851y5Fd8oLbdTIAR1QquunwlJFCk5qXQYMGYdy4cZg2bRp27dqF/Px8zJgxA3feeafrpFFpaSnS09Oxa9cu13VmsxmFhYUwmUwAgL1796KwsBBWq1WLbfoV0cZ1w8+8z6Z1RETUinLCaPLxeYhztv84SO+njBSa9XlZuXIl0tPTMXr0aGRnZ2PEiBFYunSp69cbGxtRXFyM2tpa13tLlizBL37xC0ybNg0AcO211+IXv/gF1qxZo9U2/YercZ1nbFpHREQtiZwwAoCmqFRIE1fo9pSRQpJlOaB+hLfZbIiNjUVVVRViYmJ8vR11DqyB/P7dHvruNvtm1ApcNWqC5lsiIiL/d2L3BvT5dKLndbe8iz5Db/LCjtRT8/2bs438SUYO7FdOE1paXbiGAxuJiAiAijlGjYFRhsHw4meirhC7lTeq8kPWvhAREYDAnmPUFoYXP2PoN9xj0zoFa1+IiCjQ5xi1heHF37RoWueOMrCx6Xi+9nsiIiK/1HKOkQHONtcEygmjlhhe/JGK2pfCfQdY+0JEFKSCYY5RWxhe/JRo7cvo44uxc91yBhgioiAUDHOM2sLw4qdEa1+inFWYfHwei3eJiIJQrbVUaJ2e5xi1heHFX7lqXyS3AUZJ2yzeJSIKLiaLHV+dFqthCZRTRgqGF3+WkQNp4go0hSe4XaYU75r3bfbOvoiIyKecThkb9pVBrqmAM4hOGSkYXvxdRg6qrn1SaOmB4sOsfSEiCgKllefQ/ch6TCt7ElIQnTJSMLzoQHxKX7F1dSX4fH8Za1+IiAJcTV09bi17CUD7p4ycMKD0htcC6pSRguFFB0SKd2UA48++jQjTepRWnvPW1oiIyAfiy79FvIdTRiFwIiw6yWt78iaGFz1o0biuvQCj/As8oewl1NTVe2VbRETkfSaLHYUHDgqtTcRZjXfjGwwvepGRA1vmH92mbAlAgqMcDUe3e2tXRETkRSaLHcvyj+GAPVxovSE6ReMd+QbDi45E904XWmfbw4nTRESBRjlh1KdsE+4vf9btWhkSENMb6DvMS7vzLoYXHRFN0MPPvM+mdUREAUY5YTTdPB9RjeXtrpMhNd+lH/dMwJ0yUjC86EnfYUBMKidOExEFIZETRgDgiEwBJq4IyFNGCoYXPTGEAOPc3yoE2LSOiCgQJVTs9njCCADO3vhiQAcXgOFFf1RMnGbTOiKiwNFkOyW0LlGyabwT32N40SHRidNsWkdEFBhMFjv27S0UWhuoJ4xaYnjRITatIyIKHk6njMNb38GYsjc9/Hc/sE8YtcTwokcqmtblmF+C/VydV7ZFRERdr9RajaxDzf/Nb6/exfW9IIBPGLXE8KJXgk3rejSVY8+Xa1n7QkSkU/LxHYjzUKgrAagYOjPgC3UVDC86Jtq0boJpLnauW84AQ0SkQ5ENFULrDD0GaLwT/8HwomOiRVmRTjsmH5/HxnVERDpUa0wUWhffM03jnfgPhhc9czWtc3/qX/lVNq4jItIXk8WOrwqL0eTm27UMoDEqFYZ+w723MR9jeNGz803rJLRfuKtg4zoiIn1RThnddeIvMMDZ5prm//ZL6Jb9bFAU6ioYXvQuIweYuAJOY5zQcjauIyLSB7FTRgacuelfQVOoq2B4CQQZOZDuWC60lI3riIj0QeSUkQFO1IbGeWtLfoPhJUAY+o9k4zoiogBSay0VWid6GimQMLwEChWN6yaUvYSaunqvbIuIiNQzWez46rRYDUswnTJSMLwEEsHGdQmOcjQc3e6tXRERkQpOp4wN+8og11TAyVNGbWJ4CTCijetse9awcJeIyA+VVp5D9yPrMa3sSUg8ZdQmhpcAI9q4bviZ99m0jojID9XU1ePWspcAtH/KyAkDSm94LehOGSkYXgKNq3GdZ2xaR0Tkf+LLv0W8h1NGIXAiLDrJa3vyNwwvgeZ84zpP2LSOiMj/mCx2FB44KLQ2EWc13o3/YngJRBk5sF85TWhpdSFrX4iI/IHJYsey/GM4YA8XWi9aJhCIGF4CVNQVYs9BR1V+yNoXIiIfU04Y9SnbhPvL3d89lyEBMb2bywSCFMNLgDL0G+6xaZ2CtS9ERL6lnDCabp6PqMbydtfJkJprYcY9E5SnjBQML4GqRdM6d5Tal6bj+drviYiI2iRywggAHJEpwMQVQXvKSMHwEshU1L4U7jvA2hciIh9JqNjt8YQRAJy98cWgDy4Aw0vAE619GX18MXauW84AQ0TkA022U0LrEiWbxjvRB4aXACda+xLlrMLk4/NYvEtE5GUmix3rfhD7724wnzBqSdPwYrVakZubi5iYGMTFxWHq1Kmorm6/MNRqteLhhx/GwIEDERERgT59+uD3v/89qqqqtNxmYHPVvkhuA4xyq5LFu0RE3qOcMnJWe5pjxBNGLWkaXnJzc7F//35s3LgRa9euxbZt2zB9+vR21586dQqnTp3Cc889h3379uHtt99GXl4epk6dquU2A19GDqSJK9AUnuB2GRvXERF5l/gcIwT9CaOWJFmWNXlGUFRUhIyMDHzzzTcYOnQoACAvLw/Z2dk4efIkUlNThX6fDz74AP/zP/+DmpoahIaGelxvs9kQGxuLqqoqxMTEdOrPEGjO7Pg3enw+w+O6LXG3I23yYlySHO2FXRERBa+Dp86i55tXIa6p/WLdJhhw+oZXcdHwu7y6N29T8/1bszsvBQUFiIuLcwUXABgzZgwMBgN27twp/Psof4j2gkt9fT1sNlurF7UtPqWv0Do2riMi8o7Go9sR7ya4AJxj1BbNwovZbEZycnKr90JDQ5GQkACz2Sz0e1RUVGDBggVuHzUtXLgQsbGxrldaWlqn9h3I2LiOiMh/mCx27C8+LLQ2mOcYtUV1eJk9ezYkSXL7OnhQbKiUOzabDTfffDMyMjIwf/78dtfNmTMHVVVVrldJSUmnv3bAUtm4jrUvRETaUAp1u1cfE1rPU0ateS4i+YlZs2ZhypQpbtf0798fKSkpsFgsrd53OBywWq1ISXH/D8Fut2PcuHGIjo7G6tWr0a1bt3bXGo1GGI1G4f0HvfON62IKX/e49EDxYcRn2Fn7QkTUxZRC3fFnl0NG+111ZUiQYlJ5yugnVIeXpKQkJCV5fvaWlZWFyspK7N69G0OGDAEAbN68GU6nE5mZme1eZ7PZMHbsWBiNRqxZswbh4WLTNUlc1BU5gEB4ia8rwef7y9A/MQoGg6e+j0REJEpkHABPGbVPs5qXQYMGYdy4cZg2bRp27dqF/Px8zJgxA3feeafrpFFpaSnS09Oxa9cuAM3B5cYbb0RNTQ3efPNN2Gw2mM1mmM1mNDU1abXVoCNS+yIDGH/2bUSY1qO08py3tkZEFBRExgFIAGyZf+Q4gDZo2udl5cqVSE9Px+jRo5GdnY0RI0Zg6dKlrl9vbGxEcXExamtrAQDfffcddu7cib179+KSSy5Br169XC/WsnShFrUv7QUY5S9Ujvkl2M/VeWVbRETBQnQcQHTvgRrvRJ9UPzZSIyEhAatWrWr31/v164eWbWZGjRoFjdrO0E9l5MCW+UfE7nyu3SUSgB5N5cj7ci3CxvyatS9ERF3AZLFj6w8y7hdYy0LdtnG2URCL7p0utG6CaS6HNhIRdQGOA+gaDC9BTDTRRzrtHNpIRNQFOA6gazC8BLO+w4CY1OaE7waHNhIRdQ17bR0mmF8E0P4pIycMKL3hNRbqusHwEswMIcC4ZyGh/cJdBRvXERF1jslix3dfrUdCUwXHAXQSw0uwy8gBJq6A0xgntLy6cA1rX4iIVDJZ7FiWfwz1Z08Krec4APcYXgjIyIF0x3KhpRzaSESkjlKk26dsE+6yviZ0DU8ZucfwQgAAQ/+RHNpIRKQBpUh3unk+IhyVbtfylJEYhhdqxqGNRESaEBkFAJyfYwTwlJEAhhf60fmhjSJY+0JEJEZkFAAAOCMSgIkreMpIAMMLtRJ1hdhfGta+EBGJER0FII1byOAiiOGFWhEZ2qhg7QsRkXsmix3rfhD7Ic8Qk6rxbgIHwwu1prL2RT6+Q/s9ERHpEEcBaIfhhS6koval1lqq8WaIiPSJowC0w/BCbRKtfSkx7WPhLhFRG2rq6nGr2f0pI44C6BiGF2qTSO2LDGBM2Zss3CUiakPj0e2Ib3J/yoijADqG4YXa1qL2pb1YovyFvLp4EUrO8O4LEZHCZLFjf/FhobUcBaAewwu1LyMHFUNnuf2pQQKQ0FSOrRs+5uMjIiL8WKjbvfqY0HqOAlCP4YXcMvQYILTutqOPY+e65QwwRBT0lELd8WeXe3j0zlNGHcXwQm7F90wTWhfptGPy8XmsfyGioCcyDoCnjDqH4YXcEm1ap/wFZeM6Igp2IuMAJAC2zD/ylFEHMbyQe67CXUkowHBoIxEFO9FxANG9B2q8k8DF8EKeZeRAmrgCTmOc0HIObSSiYKVqHAALdTuM4YXEZORAumO50FIObSSiYMRxAN7D8ELCDP1HcmgjEVE7OA7AexheSJzKoY2sfSGiYGKvrcME84sAOA5AawwvpI6KoY2sfSGiYGGy2PHdV+uR0FTBcQBewPBCqokObWTtCxEFA5PFjmX5x1B/9qTQeo4D6DyGF1JNtPcLwNoXIgpsSpFun7JNuMv6mtA1PGXUeQwvpJ7K2hf5+A7t90RE5ANKke5083xEOCrdruUpo67D8EIdo6L2pdZaqvFmiIh8o6auHrea3Y8CAJqDiwTwlFEXYXihDhOtfSkx7WPhLhEFpMaj2xHf5H4UAAA4IxKAiSt4yqiLMLxQh4nUvsgAxpS9ycJdIgo4Josd+4sPC62Vxi1kcOlCDC/UcS1qX9qLJcpPI1cXL0LJGd59IaLAoBTqdq8+JrTeEJOq7YaCDMMLdU5GDiqGzvI4PTWhqRxbN3zMx0dEFBCUQt3xZ5d7uPvMIl0tMLxQpxl6DBBad9vRx7Fz3XIGGCLSvZq6etxa5r5Ql6MAtMPwQp0W3zNNaF2k047Jx+ex/oWIdC+hYjfiHe4LdSUAtsw/stZFAwwv1GmiTeuUv+RsXEdEetdkOyW0Lrr3QI13EpwYXqjzXIW7klCA4dBGItIzk8WOdT+I3T1mN11tMLxQ18jIgTRxBZzGOKHlHNpIRHqknDJyVlfA6eZbKAt1tcXwQl0nIwfSHcuFlnJoIxHpkXLKaFrZk5DgbHMNC3W1x/BCXcrQfySHNhJRwBIZB+CEAaU3vMZCXQ0xvFDXUjm0kbUvRKQnIuMAQuBEWHSS1/YUjBheqOupGNrI2hci0gs14wAScVbj3QQ3TcOL1WpFbm4uYmJiEBcXh6lTp6K62v1jggceeAADBgxAREQEkpKSMGHCBBw8eFDLbZIGRIc2svaFiPRA9TgAnjLSlKbhJTc3F/v378fGjRuxdu1abNu2DdOnT3d7zZAhQ7Bs2TIUFRVhw4YNkGUZN954I5qamrTcKnUx0d4vAGtfiMj/cRyAf5FkWdbkR96ioiJkZGTgm2++wdChQwEAeXl5yM7OxsmTJ5GaKjak6vvvv8fPf/5zmEwmDBjguQ29zWZDbGwsqqqqEBMT06k/A3XSgTWQ37/b46h4APhm1ApcNWqC5lsiIuqIAyetSFl2FeKbKjyMA5AgTVzBYt0OUPP9W7M7LwUFBYiLi3MFFwAYM2YMDAYDdu7cKfR71NTUYNmyZbj44ouRltZ2C/r6+nrYbLZWL/ITrH0hogBgstjx3VfrkeAmuAAcB+BNmoUXs9mM5OTkVu+FhoYiISEBZrPZ7bWvvvoqoqKiEBUVhc8++wwbN25EWFhYm2sXLlyI2NhY16u9kEO+wdoXItIzk8WOZfnHUH/2pNB6jgPwDtXhZfbs2ZAkye2rswW2ubm52LNnD7788ktceumlmDhxIurq6tpcO2fOHFRVVbleJSUlnfra1LXU1L5cXbwIJWd494WI/INSpNunbBPusr4mdA0Ldb0jVO0Fs2bNwpQpU9yu6d+/P1JSUmCxWFq973A4YLVakZLi/h+uchflZz/7Ga655hrEx8dj9erVuOuuuy5YazQaYTQa1f4xyFvO932R37/b7TIJQEJTOT7d8DGG33gbLkmO9s7+iIjaoRTpTjHP97hWhgQpJpWFul6iOrwkJSUhKclz852srCxUVlZi9+7dGDJkCABg8+bNcDqdyMzMFP56sixDlmXU19er3Sr5i/O1LzGFr3tcetvRx/F/66qBm+9lgCEinxLppgucDy4AxwF4kWY1L4MGDcK4ceMwbdo07Nq1C/n5+ZgxYwbuvPNO10mj0tJSpKenY9euXQCAo0ePYuHChdi9ezdOnDiBHTt24I477kBERASys7O12ip5gWjtS6TTjsnH57H+hYh8TqSbLgA4IxIAnjDyKk37vKxcuRLp6ekYPXo0srOzMWLECCxdutT1642NjSguLkZtbS0AIDw8HF999RWys7NxySWXYNKkSYiOjsaOHTsuKP4lfRGtfVH+I8HeL0TkS2q66UrjFjK4eJnqx0ZqJCQkYNWqVe3+er9+/dCyzUxqairWr1+v5ZbIV1y1L/dAbm7j1C5l7pFp32aksfcLEXmZUqibJtpNN0asbxl1Hc42Iu/JyIE0cQWcxjih5ez9QkS+wG66/o/hhbwrIwfSHcuFlrL3CxH5gkihruu/SizS9QmGF/I6Q/+RnHtERH5LpFCX3XR9i+GFvO98/YsnSu2Led9m7fdERAR1hbrspus7DC/kG5x7RER+RinU7S5aqMtuuj7D8EI+w7lHRORPWKirHwwv5DNq5h6x9oWItMZCXf1geCHfYe0LEfkRFurqB8ML+RZrX4jID7BQV18YXsjnWPtCRL7EQl39YXghn1NT+3J18SKUnOHdFyLqOizU1R+GF/I9FbUvCU3l2LrhYz4+IqIuY6+twwTziwBYqKsXDC/kH1TUvtx29HHsXLecAYaIOs1kseO7r9YjoamChbo6wvBCfkO09iXSacfk4/NY/0JEnWKy2LEs/xjqz54UWs9CXf/B8EJ+Q7T2RfnpiL1fiKijlCLdPmWbcJf1NaFrWKjrPxheyH+4al8koQDD3i9E1FFKke5083xEOCrdrmWhrv9heCH/kpEDaeIKOI1xQsvZ+4WIOkKkmy7QHFwkgIW6fobhhfxPRg6kO5YLLWXvFyLqCJFuugDgjEgAJq5goa6fYXghv2ToP5Jzj4hIE2q66UrjFjK4+CGGF/JPnHtERBpQ3U03JlXbDVGHMLyQ/+LcIyLqYuymGxgYXsivce4REXUlkUJddtP1fwwv5NfUzD1i7QsReSJSqMtuuv6P4YX8G2tfiKiLqCnUZTdd/8bwQv6PtS9E1EmqC3XZTdevMbyQLrD2hYg6o7TyHCKOrGOhboBgeCFdUFP7cnXxIpSc4d0XIvpR0amzGH/qRQAs1A0EDC+kDypqXxKayrF1w8d8fEREAJprXYp3bkCSfIaFugGC4YX0Q0Xty21HH8fOdcsZYIiCnFLrMqhqu9B6FurqA8ML6Ypo7Uuk047Jx+ex/oUoyClN6UbbPhJaz0JdfWB4IV0RrX1Rbg1nFi9i7xeiIGavrcME84se17FQV18YXkhfXLUvklCAiW8qR/2WZ72wMSLyNyaLHd99tR4JTRUep0cDMgt1dYThhfQnIwfSxBVwGuOElg/Y/zJOF7yn7Z6IyK+YLHYsyz+G+rMnhdbLmb9joa6OMLyQPmXkQLpjufDyqK1/gdPh0HBDROQvlCLdPmWbcJf1NaFrDOk3a7wr6koML6Rbhv4jhetfouvLsO/rz7yxLSLyMaVId7p5PiIclW7XstZFnxheSL8Ee78oyr9dzaPTREFAZHI00BxcJIC1LjrE8EL6lpHT3FRKwPWVH/HoNFEQEJkcDQDOiARg4grWuugQwwvpXvQNc1Adliw0OiDz0D94dJoogKmZHC2NW8jgolMML6R7htBQ2H/1lMd1EoB4hwXmfZu13xQReZ3qydExqdpuiDTD8EIBoVfWJJwaeJ/Q2urCNax9IQpAnBwdPBheKGD0yvyN0LpRlR+y9oUoAHFydPBgeKGAITo6AACGHXwKJeWVWm+JiLyEk6ODi6bhxWq1Ijc3FzExMYiLi8PUqVNRXS1WLCnLMm666SZIkoRPPvlEy21SoBA8Oi0BiHFWIfH1K9l5lygAcHJ08NE0vOTm5mL//v3YuHEj1q5di23btmH69OlC1y5evBiS5HkaBVErGTmwXzlNaGl3RyVSNkxngCHSOU6ODj6ahZeioiLk5eXhjTfeQGZmJkaMGIGXX34Z7777Lk6dOuX22sLCQjz//PN46623tNoeBbCoK8RuB0tofv7N0QFE+tayKZ07LNQNHJqFl4KCAsTFxWHo0KGu98aMGQODwYCdO3e2e11tbS0mT56MV155BSkpTMeknpraFwM4OoBI70Sb0nFydODQLLyYzWYkJye3ei80NBQJCQkwm83tXvfoo49i2LBhmDBhgtDXqa+vh81ma/WiIOeqfZGEAgzA0QFEeqWmKR0nRwcO1eFl9uzZkCTJ7evgwYMd2syaNWuwefNmLF68WPiahQsXIjY21vVKS0vr0NemAJORA2niCjjDE4SWc3QAkf6obkrHydEBI1TtBbNmzcKUKVPcrunfvz9SUlJgsVhave9wOGC1Wtt9HLR582YcOXIEcXFxrd6/7bbbMHLkSGzduvWCa+bMmYOZM2e6/rfNZmOAoWYZOZAuGYvafwxERONZj7eUm0cH3IW0xGivbI+IOufk2VqEFH/qakrXfm8XCVJMKmtdAojq8JKUlISkpCSP67KyslBZWYndu3djyJAhAJrDidPpRGZmZpvXzJ49G/fff3+r9y6//HK88MILGD9+fJvXGI1GGI1GlX8KChaGMCOqrn8WERvcn3JTRgeY9m1G2iixR5ZE5Dsmix0rd/yA35a9DIBN6YKNZjUvgwYNwrhx4zBt2jTs2rUL+fn5mDFjBu68806kpjbPkygtLUV6ejp27doFAEhJScHgwYNbvQCgT58+uPjii7XaKgU4jg4gCiwmix3L8o/BWLoDPcGmdMFI0z4vK1euRHp6OkaPHo3s7GyMGDECS5cudf16Y2MjiouLUVtbq+U2iFSNDji8dRVrX4j8lFLn0qdsE/5g/bvQNWxKF3hUPzZSIyEhAatWrWr31/v16wdZdv9NwtOvE4lQjk+H1px2+1OaDGDIgWeRf3gCRg7kUX0if6MMX7zPPF/4GjalCzycbUTBQXB0gAFAMs6gcsNCPj4i8kMiwxcVbEoXuBheKHioGB1wi/VtHp0m8jOiwxcB/Hj6iIW6AYnhhYKK6OgAALi6eBFKzvDuC5E/UDt8ERHxwMQVLNQNUAwvFFRERwdIABKayrF1w8d8fETkB5RaF9Hhi9LtbzO4BDCGFwougrUvituOPo6d65YzwBD5WMtaF3dcdS4Xj/TCrshXGF4o+GTkQL5ujtDSSKcdk4/P4/FpIh9SU+vC4YvBgeGFgpLhuj8JPz768fh0mRd2RkQtKbUuEfUVQus5fDE4MLxQcFIxeZrHp4l8p7TyHI6UV2NAiNgPDxy+GBwYXih4KZOnjXFCy3l8msj7ahocGHh2C0adfsPtDxrs6RJcGF4ouGXkQLpjufDy5snT1RpuiIhaqqiqxW84fJF+guGFgp6h/0jh+pd4hwXmfZu9sS2ioGey2FEkUKgrAZCvm81alyDC8EKk8vg0J08TaU8p1L34zJdC6w2Jl2i8I/InDC9EgKrj05w8TaS9k2drEVL8KUZXiTWlQ1RPbTdEfoXhheg80ePTPDpNpC2TxY5lXx3Br8/XurjDQt3gxPBCpODkaSKfM1nsWJZ/DMbSHegJNqWjtjG8ELXEydNEPqPUufQp24Q/WP8udA2b0gUnhhein1AzeXrYwadQUl6p3WaIgogyfHG6eT7Cm2xC17ApXXBieCH6CTWTp2OcVUh8/UqcLnjPG1sjCmgthy96elzEWpfgxvBC9FMqj053d1QiZcN0BhiiTlAzfFHG+XDDWpegxfBC1BYVR6eV4Y1RW/8Cp8Oh6baIApFS6zKoarvYBRHxwMQVrHUJYgwvRO0QPToNNP9Fiq4vw76vP9N6W0QBR6l1GW0T6+ki3f42g0uQY3ghao+KydOK8m9X8/g0kUota13ccdW5XDzSC7sif8bwQuSOMnk6PEFo+fWVH7H7LpEKampd2NOFFAwvRJ5k5ECaeRC13eLZfZeoC6mtdWFPF1IwvBAJMIQZUXX9s57Xgd13iUSprXVhTxdSMLwQCeqVNQmnBt4ntPYW69t8fETkgepaF/Z0ofMYXohU6JX5G+G1fHxE1D7WulBnMLwQqaCm+y4fHxG1zeFw4v1vSjDA+qXQeta60E8xvBCpobL7Loc3ErVmstixaEMxav67GjfVfCJ0DWtd6KcYXojUUtF9F+DwRiKFyWLHsvxjOFhajj82LPG4nrUu1B6GF6IOEO2+y+GNRM2UY9F9yjbh1bL/QTxsrHWhDmN4IeoIDm8kUkU5Fj3dPB+RTVVC17DWhdrD8ELUUR0Z3rjlcQ5vpKDU8li05zsuzVjrQu1heCHqBNXDGxssOLHmSa23ReRX1B2LZq0LecbwQtQZHRje2Pf7F/n4iIKG6hEAOH9nhrUu5AbDC1FnqRzeCPDxEQUPtSMApO6JwMQVrHUhtxheiLqCiuGNEvj4iIKH+AgAAN0TgZlFDC7kEcMLURcRHd6o4OMjCnRqa11wywtAaJjW26IAwPBC1IV6ZU3Cicv/ILyej48oUDmdMvL2mfGzs9uE1vNYNKnB8ELUxdIm/BX2sGQ+PqKgtuNIBSp3f4Sx1auF1vNYNKnB8ELUxQyhoaj+1VPC6/n4iAKNyWLHOzt/wLSapR7X8lg0dQTDC5EG1D4+iv7iMTjq6jTcEZF3KEejr7f8Gz0hUuvCEQCkHsMLkUbUPD6KcpxF/XMDeQeGdO/k2VqEFH+K39hWCK1nrQt1hKbhxWq1Ijc3FzExMYiLi8PUqVNRXV3t9ppRo0ZBkqRWr9/+9rdabpNIE2ofH3H+EemdyWLHsq+O4NdlLwtfw1oX6ghNw0tubi7279+PjRs3Yu3atdi2bRumT5/u8bpp06bh9OnTrteiReID8Ij8iZrHR5x/RHpmstixLP8YjKU7hB4XyQBrXajDNAsvRUVFyMvLwxtvvIHMzEyMGDECL7/8Mt59912cOnXK7bXdu3dHSkqK6xUTE6PVNok0J/r4COD8I9In5Vh0z9LP8bBV/G4ja12oozQLLwUFBYiLi8PQoUNd740ZMwYGgwE7d+50e+3KlSuRmJiIwYMHY86cOaitrW13bX19PWw2W6sXkT9p+fjIKXhN3+9fxCk+PiKdUI5FP1zxJLo32YWukUbNZa0LdVioVr+x2WxGcnJy6y8WGoqEhASYzeZ2r5s8eTL69u2L1NRUfP/993jsscdQXFyMjz/+uM31CxcuxN/+9rcu3TtRV+uVNQmnAcRs+jMimyqFrjFunItDfcfi0tQ4LbdG1CnKsei/nj8WLfK4SIpOBa79o+Z7o8Cl+s7L7NmzLyio/enr4MGDHd7Q9OnTMXbsWFx++eXIzc3FihUrsHr1ahw5cqTN9XPmzEFVVZXrVVJS0uGvTaSlXlmTYPxTMWpC44ROIPVwVsD00XyYLGI/yRJ5m/K46NrTy4XrXCRIwE3P8nERdYrqOy+zZs3ClClT3K7p378/UlJSYLFYWr3vcDhgtVqRkpIi/PUyMzMBACaTCQMGDLjg141GI4xGo/DvR+RLoeHhKB+9CN03eC5cB4CbzixD3tZB6H/7dBgMQtNhiLxGeVz0UM1/xC6IiAfGv8THRdRpqsNLUlISkpKSPK7LyspCZWUldu/ejSFDhgAANm/eDKfT6QokIgoLCwEAvXr1UrtVIr/UK2sSjp/aj757PU/aBYAhB55F/uEJGDlQPPQTae2nj4tESLe/DQwYpdmeKHhoVrA7aNAgjBs3DtOmTcOuXbuQn5+PGTNm4M4770RqaioAoLS0FOnp6di1axcA4MiRI1iwYAF2796NY8eOYc2aNbjnnntw7bXX4oorrtBqq0Rep6aBXTLOoHLDQj4+Ir/RkcdFiOkNXDzSC7ujYKBpn5eVK1ciPT0do0ePRnZ2NkaMGIGlS39M6Y2NjSguLnadJgoLC8OmTZtw4403Ij09HbNmzcJtt92GTz/9VMttEnmd2gZ2t1jfxn8//zccDtHzSkTaUR4XTRR9XATwWDR1KUmWZZH2E7phs9kQGxuLqqoq9ochv1ex7kkkfvO8x3UygLOIwdIhn+L2zAG4JDla+80RtcFkseOFz4vwV9OdSBaaXQRg1Fxg1GNab410Ts33b842IvKhxJvmoTGyl9DjowTY8OCeHOxct5yPkMgnlKGLF9kKxR8X8Vg0aYDhhciXDCHodrP4+ItoZxUmH5+Hw1v+A6czoG6akg6cPFuL70srkdXgvtFoKzwWTRpgeCHytYwcyNfNEVoqnX/dWDQXBzf/W9NtEbVkstjx1vZj6HF8A66r/FDoGnbRJa0wvBD5AcN1fxJ6fKQIgRODtj/MEQLkFcrQxePlVvzZscTjej4uIq0xvBD5A9fjI0k4wADnRwicqtRoU0Sthy6+fDoXcbCJFenycRFpiOGFyF9k5ECauAKI6CG0nCMEyBtaDl2MbKoSuka65kE+LiJNMbwQ+ZOMHEizDsIR3kP4DsxNZ5bh8NZVLOClLnfIbMdb20yYVvMvAJ6HLroMzNZsT0QAwwuR/wkNQ2jOYlWXNI8QKNNmPxSUDpXZsGDtAVxd+hZ6wioYXKTmTrp9h2m8Owp2DC9E/igjB/Ltb8Mp8FdUGSFQtu4pbD9czjsw1Gkmix2vbDmCi8yb8IDzfaFrXP/WsZMueQHDC5GfMgz+NcpufFX48dFttn/jh4/+ite2FLMGhjpMKdA9ZbXjUcebwtdJ3ROBiStY60JewfBC5Md6DbsLZ66aJbRWAnB33SrcteNmduGlDttxpALr957GOOtKofb/MgB0TwRmFjG4kNcwvBD5OdERAor4pormLrws4iWVTBY7Vu06gcvt2/D/HO+KX3jLC0BomHYbI/oJhhcif6dyhICE5p+GWcRLajgcTrz/TQkqqmowq+kt4evYRZd8geGFSA9UjBAAmv9iJ+MMytf/HYfKbNrtiwKCyWLHog3F+GyfGWOtK5Esc+gi+TeGFyKdUDtCAAB+XbUCee/9C4fMrH+htimt/4tOWXGf4z3hx0USwC665DMML0R60YERAhKAh6xPY/v/vcECXrpAy9b/L5nvwf9rfFe8ER0fF5EPMbwQ6YkyQiC6l/AlIXDivtPzWcBLF2jZ+j+uqULoGj4uIn/A8EKkNxk5kB7dD4yaq+oREgt4qaWOtv7n4yLyBwwvRHpkCAFGPSZcxMsuvNRSx1r/n8fHReQHGF6IdExtES+78FJHWv+78HER+QmGFyI960APmLvrVmFSfja+/L+3eIw6yHS09X8ziY+LyG8wvBDpXUYOpNuXQ5bE/zr3cJ7B/yv9K49RBxm1rf9dYnpzbhH5FYYXokAw+FZIty9TdYRaOUb9xUf/4h2YAOd0yvjqcDmWbDuCwVVbhHu5yEBzjcsjexlcyK8wvBAFistuVdWFF2g+Rv3b8gW8AxPATBY7Xt1iwsL1B5F6cgMWNr0gfrJo1Fxg1GN8VER+h+GFKIB0pAuvcgfm8w+W8CRSgFG6535z3Iqrzm3Hs/I/ESJ5/ufLXi7k7xheiAJJB7rwAs13YB468xRPIgUQpTj35NlaRIc24ZG6V4WvZS8X8ncML0SBpgNdeAGeRAo0SnFuP8tmLDg6CfGwsfU/BQyGF6JA1MEuvABPIgWCQ2Y73vzqBwyu3IL5dc8gDmJBlI+LSC8YXogC1fkuvGqPUfMkkr4p3XOTT36Ghc4XXP88RfBxEekFwwtRoFN5jFqhnET67P3XeQdGB5Tj0E+vL0LvU3l4xilWnOsihQB3LOfjItIFhheiYHDZrarvwCgmnflfPJe3n3dg/FjL49BJJ/LwdxXHoV3x5ra3gMtu1WaDRF2M4YUoWLS4A6OmmV0KrLjl2EI89ek+3oHxQ4fMdrz8hQnbik/jNvt/sEjwOLRC6p4ITPw3MPhW7TZJ1MUkWZYDqqmDzWZDbGwsqqqqEBMT4+vtEPmfA2sgf/ZnSPbTqi6rRBT+kzgTV469B8MGJMJgUDWLmDRwqMyGBZ8W4SLzJjzqeAPJsApfK+N8cJlZBISGabdJIkFqvn/zzgtRsOngSaRYuRoPVTzJXjB+4pDZjn/kFSP1VB6edixCkorgApwvzr3lBQYX0iWGF6Jg1IGTSJLEXjD+QjlRlHBsPZ5uUneiCACLc0n3GF6IglkHTyIpvWA++c+r2FbMkQLe1PKOyzMq61tcWJxLOsfwQhTsLrsV0qi5qi5RftKfZXsWn3+wBE+tO8DHSF7Q1h0XVZQ7LizOJZ1jeCGi5o6qManqe8FITixwPIfG7z/GS1+Y+BhJIxf0cFF5x4XHoSnQMLwQUXMNzLhnIUH8GLVCAvC3hucx+NArPE7dxZTQ8rdP9+HJT/er7uGikGJ68zg0BRQelSaiHx1YA3z6e+Dc2Q5dzuPUXcdksWPV1yewpdiCmrp63OP4EA9JH6h/VDRqbvOdNbb8Jz+n5vs3wwsRteZsArY9B/nrVyHVVaq6VJYBWQJWdLsLxy77HcZclsoQ0wGHzHb87+bD+O/JSgxvLMCjjW+oPgoNKQS4nY+JSD8YXhheiDpPCTFbn1b/0z6AMiTgFeM0hA6egMmZfXBJcnSXbzHQOJ0yvjKVY/GmQzhx5hyubczHPw0vAFB5FBoAbmdhLukLwwvDC1HX2fcJ5I/ugyQ7VV2m/Iflr93+iKr+t2DG9QNwaU/+nWyP8pjo8wNmWKvr8JDhY/xO+ggGtUeheceFdMovOuxarVbk5uYiJiYGcXFxmDp1Kqqrqz1eV1BQgOuvvx6RkZGIiYnBtddei3Pnzmm1TSLypIO9YJTj1H9reB4Zxa9g7oeF7AnTBqUo9/nPi7G52IIRjq+RHzodDxk+VB9cAJ4ooqCg2Z2Xm266CadPn8a//vUvNDY24r777sNVV12FVatWtXtNQUEBxo0bhzlz5mD8+PEIDQ3Ff//7X0yYMAFGo1Ho6/LOC5FGOngHRlEtG/FOyK9xOH06xlzWG4N6xaB3XETQ1sM4nTLyj1Rg0wEzdhw5g7O1jbi2MR/PSx18TMQ7LqRzPn9sVFRUhIyMDHzzzTcYOnQoACAvLw/Z2dk4efIkUlNT27zummuuwQ033IAFCxZ0+GszvBBpaP8nwAf3Ng/16+BvcVaOwj/CHsTx5NH4WXI0xmQkB1VRrxJaPtp9Et8eP4uGhgZc5tiPG6RvMUn+THXHXNc/C9a4kM75/LFRQUEB4uLiXMEFAMaMGQODwYCdO3e2eY3FYsHOnTuRnJyMYcOGoWfPnrjuuuuwfft2t1+rvr4eNput1YuINHLZrcDEf0OKiO/wbxGHajzVuAgjSt9E3vclmP3R95j5fiG2Hw78R0omix1PrT2Av6zei81FpzGpZhU2Nk3FMulJTMb6DrX6Zw8XCkaahBez2Yzk5ORW74WGhiIhIQFms7nNa44ePQoAmD9/PqZNm4a8vDz88pe/xOjRo3H48OF2v9bChQsRGxvreqWlpXXdH4SILpSRA/zpSPNU6vA41ZdLUvN/eH6H97GhaSom1b6DL/afwmMBHmIOme14adNhfHGwDNfU78CX0jQ8bPgAsfBcC9iuUXOBR/ZywCIFHVXhZfbs2ZAkye3r4MGDHdqI09n8HP2BBx7Afffdh1/84hd44YUXMHDgQLz11lvtXjdnzhxUVVW5XiUlJR36+kSkgjKV+s9Hm0NMB3+bWFTjYcMHKDDch0k172DzgdOYt3ovHvvov/h8vxkl1lpdBxmnU0aJtRZ5+09j3urv8fUPZ/DLmm1Y6PgH4uROhBZlRtGox9h8joJSqJrFs2bNwpQpU9yu6d+/P1JSUmCxWFq973A4YLVakZKS0uZ1vXr1AgBkZGS0en/QoEE4ceJEu1/PaDQKF/MSURdTQkziwE4V80ZJ9fh9yAeYijVYVpOD1/f9BgVHzqBvj0hd1sUodS1fFJXhsKUaRy3VsJ2rx4yQj/GA9FGH64VceKKIgpyq8JKUlISkpCSP67KyslBZWYndu3djyJAhAIDNmzfD6XQiMzOzzWv69euH1NRUFBcXt3r/0KFDuOmmm9Rsk4i8bfCtkCR0upg3EvWYIX2Ae+VP8Und9dh26mrkmQdhU5EZQ/sl4PYhF/lliHE6ZZRWnoO9vhEHT9uxtbgc3504C0djAwY3FeF38i782rAF0ehk24eIBGD8i3xMREFP06PSZWVlWLJkieuo9NChQ11HpUtLSzF69GisWLECV199NQBg8eLFeOKJJ/Dmm2/iyiuvxPLly/Hcc89h3759GDBggNDX5WkjIh/q5GyktlQhCiucN2Gp/GvERIbjqn4J+M0ve6Nfj0jUNjYhMizUJ0eulcBSZLbh2x+sOFJeDVN5DcptdXA6m/CgYTXuDcnrXE2LiwRc9xhw3Z/5mIgClprv36ruvKixcuVKzJgxA6NHj4bBYMBtt92Gl156yfXrjY2NKC4uRm1treu9Rx55BHV1dXj00UdhtVrx85//HBs3bhQOLkTkYxk5QPrNzWMFdrwIqaGm07+lUhdzn/x/2FCTha8PXI4VBxNxPOoKpMRFontYKFJiwnFlnzgMTIlGdHg3TcLMT++uFJZU4kh5NU6cqUVDQwN+Lhchy1mBq6W9GBv6NSKl+q774re/zdNERC1wPAARaaMTAx5FWOVo5BmuxfaQq/FV46VwygYkRoXhovju+FlyNK4flIR+PSJR3eBAdZ0DUcbQdoNNy2BSXedA97AQ1DY0IcoYikhjKI6fqcHmgxYctlTj5NlzqLDXw4AmXG04iF/hW2RjOxKgQZuGmN7AuGf4mIiCgs+b1PkSwwuRnzkfYrD16U7Vw7hTiUh80TQUBRiMM4YeKJQyIEshiA4PRYhBQpNTRnioAckx4bgkKcp1l+anwaTcXg/buUY0NsnoFiLBGBoCpyyjut4BydmEn8sH0EM+g2HYh+ul3YiTuuKR0E+ERQO/vBsYmA30HcbHRBQ0GF4YXoj8jwb1MO05K0fi385x+FZOR6+QKqR2q4HF0R3RThusiEYCqlHXLR5WQwLqGh3ogUrEwYYqRCEW1bA6IxEvVeOMHAOzMxZXSQdxj2GDNmHFhXUtFNwYXhheiPyTchdmx4tAF9TDBBS296cg5/PxAEREbTrfFwazS5q7w4ZF+npHvheRwPb+RCoxvBCR9/00xHRiVpJuRcQ3/9n/ZGJBLpFKfGxERL7nbAKO7wCK1wPf/RtosPt6R9pgMS5Ru1jzwvBCpF+BWBfTLRIY/gfg2j8ysBC1g+GF4YVI/5QQs/M1r5xQ0kREPJD5O4YWIgEMLwwvRIFDeaRkPw3UlAOVJcCe//jfo6WwaOAXuUBcHyAyCYjuxUdDRCr4xXgAIqIuYQgBLh7Z+r2xf/efuzK8u0LkdbzzQkT61fKuzNEtQPFn2oeZ8Dhg4M3AgFG8u0LUhXjnhYiCQ8u7MldM/DHMVJcB3RMBSWr+/2vKge49gNozP/7fyCQgMll8TU05ENWTYYXIDzC8EFHgaOsRExEFHDapIyIiIl1heCEiIiJdYXghIiIiXWF4ISIiIl1heCEiIiJdYXghIiIiXWF4ISIiIl1heCEiIiJdYXghIiIiXQm4DrvKqCabzebjnRAREZEo5fu2yMjFgAsvdrsdAJCWlubjnRAREZFadrsdsbGxbtcE3FRpp9OJU6dOITo6GpIkdenvbbPZkJaWhpKSEk6s1hA/Z+/g5+wd/Jy9h5+1d2j1OcuyDLvdjtTUVBgM7qtaAu7Oi8FgwEUXXaTp14iJieFfDC/g5+wd/Jy9g5+z9/Cz9g4tPmdPd1wULNglIiIiXWF4ISIiIl1heFHBaDTiiSeegNFo9PVWAho/Z+/g5+wd/Jy9h5+1d/jD5xxwBbtEREQU2HjnhYiIiHSF4YWIiIh0heGFiIiIdIXhhYiIiHSF4eUnXnnlFfTr1w/h4eHIzMzErl273K7/4IMPkJ6ejvDwcFx++eVYv369l3aqb2o+59dffx0jR45EfHw84uPjMWbMGI//XKiZ2n+fFe+++y4kScKtt96q7QYDhNrPubKyEg899BB69eoFo9GISy+9lP/tEKD2c168eDEGDhyIiIgIpKWl4dFHH0VdXZ2XdqtP27Ztw/jx45GamgpJkvDJJ594vGbr1q345S9/CaPRiEsuuQRvv/225vuETC7vvvuuHBYWJr/11lvy/v375WnTpslxcXFyWVlZm+vz8/PlkJAQedGiRfKBAwfkxx9/XO7WrZu8d+9eL+9cX9R+zpMnT5ZfeeUVec+ePXJRUZE8ZcoUOTY2Vj558qSXd64vaj9nxQ8//CD37t1bHjlypDxhwgTvbFbH1H7O9fX18tChQ+Xs7Gx5+/bt8g8//CBv3bpVLiws9PLO9UXt57xy5UrZaDTKK1eulH/44Qd5w4YNcq9eveRHH33UyzvXl/Xr18vz5s2TP/74YxmAvHr1arfrjx49Knfv3l2eOXOmfODAAfnll1+WQ0JC5Ly8PE33yfDSwtVXXy0/9NBDrv/d1NQkp6amygsXLmxz/cSJE+Wbb7651XuZmZnyAw88oOk+9U7t5/xTDodDjo6OlpcvX67VFgNCRz5nh8MhDxs2TH7jjTfke++9l+FFgNrP+bXXXpP79+8vNzQ0eGuLAUHt5/zQQw/J119/fav3Zs6cKQ8fPlzTfQYSkfDy5z//Wb7ssstavTdp0iR57NixGu5MlvnY6LyGhgbs3r0bY8aMcb1nMBgwZswYFBQUtHlNQUFBq/UAMHbs2HbXU8c+55+qra1FY2MjEhIStNqm7nX0c37yySeRnJyMqVOnemObuteRz3nNmjXIysrCQw89hJ49e2Lw4MF4+umn0dTU5K1t605HPudhw4Zh9+7drkdLR48exfr165Gdne2VPQcLX30fDLjBjB1VUVGBpqYm9OzZs9X7PXv2xMGDB9u8xmw2t7nebDZrtk+968jn/FOPPfYYUlNTL/gLQz/qyOe8fft2vPnmmygsLPTCDgNDRz7no0ePYvPmzcjNzcX69ethMpnw4IMPorGxEU888YQ3tq07HfmcJ0+ejIqKCowYMQKyLMPhcOC3v/0t5s6d640tB432vg/abDacO3cOERERmnxd3nkhXXnmmWfw7rvvYvXq1QgPD/f1dgKG3W7H3Xffjddffx2JiYm+3k5AczqdSE5OxtKlSzFkyBBMmjQJ8+bNw5IlS3y9tYCydetWPP3003j11Vfx3Xff4eOPP8a6deuwYMECX2+NugDvvJyXmJiIkJAQlJWVtXq/rKwMKSkpbV6TkpKiaj117HNWPPfcc3jmmWewadMmXHHFFVpuU/fUfs5HjhzBsWPHMH78eNd7TqcTABAaGori4mIMGDBA203rUEf+fe7Vqxe6deuGkJAQ13uDBg2C2WxGQ0MDwsLCNN2zHnXkc/7LX/6Cu+++G/fffz8A4PLLL0dNTQ2mT5+OefPmwWDgz+5dob3vgzExMZrddQF458UlLCwMQ4YMwRdffOF6z+l04osvvkBWVlab12RlZbVaDwAbN25sdz117HMGgEWLFmHBggXIy8vD0KFDvbFVXVP7Oaenp2Pv3r0oLCx0vXJycvCrX/0KhYWFSEtL8+b2daMj/z4PHz4cJpPJFQ4B4NChQ+jVqxeDSzs68jnX1tZeEFCUwChzpF+X8dn3QU3LgXXm3XfflY1Go/z222/LBw4ckKdPny7HxcXJZrNZlmVZvvvuu+XZs2e71ufn58uhoaHyc889JxcVFclPPPEEj0oLUPs5P/PMM3JYWJj84YcfyqdPn3a97Ha7r/4IuqD2c/4pnjYSo/ZzPnHihBwdHS3PmDFDLi4ulteuXSsnJyfLTz31lK/+CLqg9nN+4okn5OjoaPmdd96Rjx49Kn/++efygAED5IkTJ/rqj6ALdrtd3rNnj7xnzx4ZgPzPf/5T3rNnj3z8+HFZlmV59uzZ8t133+1arxyV/tOf/iQXFRXJr7zyCo9K+8LLL78s9+nTRw4LC5Ovvvpq+euvv3b92nXXXSffe++9rda///778qWXXiqHhYXJl112mbxu3Tov71if1HzOffv2lQFc8HriiSe8v3GdUfvvc0sML+LUfs47duyQMzMzZaPRKPfv31/++9//LjscDi/vWn/UfM6NjY3y/Pnz5QEDBsjh4eFyWlqa/OCDD8pnz571/sZ1ZMuWLW3+91b5bO+99175uuuuu+CaK6+8Ug4LC5P79+8vL1u2TPN9SrLM+2dERESkH6x5ISIiIl1heCEiIiJdYXghIiIiXWF4ISIiIl1heCEiIiJdYXghIiIiXWF4ISIiIl1heCEiIiJdYXghIiIiXWF4ISIiIl1heCEiIiJdYXghIiIiXfn/NrmEWC6saYIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Test 2\n",
    "u0 = torch.from_numpy(np.sin(beta2 * X[0])).float().unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "u[0] = u0\n",
    "u[:, 0] = ux0\n",
    "u[:, -1] = uxn\n",
    "\n",
    "b = np.zeros(nx - 1)\n",
    "for j in range(1, nt + 1):\n",
    "    b[0] = r * u[j - 1, 0] + r * u[j, 0]\n",
    "    b[-1] = r * u[j - 1, -1] + r * u[j, -1]\n",
    "    u[j, 1:nx] = Ainv @ ((B @ u[j - 1, 1:nx]) + b)\n",
    "\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), u[-1], alpha=0.5)\n",
    "# plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta2_vec, u0), 1)).detach())\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), model(torch.cat((beta2_vec, vec), 1)).detach())\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What does the Fourier Layer do?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch.utils.hooks.RemovableHandle at 0x222847e77f0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "activation = {}\n",
    "def get_activation(name):\n",
    "    def hook(model, input, output):\n",
    "        activation[name] = output.detach()\n",
    "    return hook\n",
    "\n",
    "model.k0.register_forward_hook(get_activation('k0'))\n",
    "model.w0.register_forward_hook(get_activation('w0'))\n",
    "model.k1.register_forward_hook(get_activation('k1'))\n",
    "model.w1.register_forward_hook(get_activation('w1'))\n",
    "model.k2.register_forward_hook(get_activation('k2'))\n",
    "model.w2.register_forward_hook(get_activation('w2'))\n",
    "model.k3.register_forward_hook(get_activation('k3'))\n",
    "model.w3.register_forward_hook(get_activation('w3'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "upredt0 = model(torch.cat((beta0_vec, vec), 1))\n",
    "# print(activation['k0'].shape)\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['k0'][0], axis=0))\n",
    "plt.subplot(122)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['w0'][0], axis=0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['k1'][0], axis=0))\n",
    "plt.subplot(122)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['w1'][0], axis=0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['k2'][0], axis=0))\n",
    "plt.subplot(122)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['w2'][0], axis=0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['k3'][0], axis=0))\n",
    "plt.subplot(122)\n",
    "plt.scatter(np.linspace(0, 1, nx + 1), torch.mean(activation['w3'][0], axis=0))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.3220, -0.3408, -0.3596, -0.3770, -0.3915, -0.4021, -0.4083, -0.4100,\n",
       "        -0.4077, -0.4021, -0.3944, -0.3857, -0.3773, -0.3698, -0.3640, -0.3599,\n",
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       "        -0.2804, -0.2809, -0.2813, -0.2814, -0.2809, -0.2799, -0.2784, -0.2766,\n",
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       "        -0.2774, -0.2774, -0.2767, -0.2752, -0.2733, -0.2714, -0.2697, -0.2688,\n",
       "        -0.2687, -0.2695, -0.2711, -0.2730, -0.2748, -0.2759, -0.2760, -0.2749,\n",
       "        -0.2728, -0.2702, -0.2677, -0.2664, -0.2673, -0.2712, -0.2787, -0.2899,\n",
       "        -0.3047])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.mean(activation['k0'][0], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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